I managed to bisect mesa and got this result:

https://cgit.freedesktop.org/mesa/mesa/commit/?id=fb827c055cb1bdd2b18d0687c06c56b537d805f3
is the first bad commit
commit fb827c055cb1bdd2b18d0687c06c56b537d805f3
Author: Nicolai Hähnle <nicolai.haehnle@amd.com>
Date:   Mon Sep 12 12:19:47 2016 +0200

    winsys/radeon: enable buffer allocation from slabs

    Only enable for chips with GPUVM, because older driver paths do not take
the
    required offset into account.

    Reviewed-by: Marek Olšák <marek.olsak@amd.com>

:040000 040000 4e1327d4b72890178a2057d2341971001f2de54d
d162404a219307e5f6cda1009b864e66f23f4e63 M      src

I have also noticed that after a recent update the game now gives some more
information, so when it does run like described in comment #3, it now also
tells me that it detected an error by adding the following line right after the
four driver error blocks:

   2.321 glTexImage2D for format ARGB_8888, size 8192x8185 failed
(GL_OUT_OF_MEMORY)